Generalized band matrices and their inverses
Identifieur interne : 001673 ( Main/Exploration ); précédent : 001672; suivant : 001674Generalized band matrices and their inverses
Auteurs : P. Favati [Italie] ; G. Lotti [Italie] ; F. Romani [Italie] ; P. R Zsa [Hongrie]Source :
- CALCOLO [ 0008-0624 ] ; 1991-03-01.
Abstract
Abstract: The idea of defining the generalized band matrices is based on the recognition that several pattern matrices and their inverses have low rank submatrices in certain domains. Theoretical considerations concerning the generalized band matrices enable us to give uniform treatment for several well known classes of matrices like band matrices, block band matrices, band matrices with low rank corrections, sparse matrices and their inverses. Making use of the new notions of information content and of compact representation of matrices, the concept of proper matrices is extended for generalized band matrices. Some reduction algorithms are presented which help to discover certain hidden structural properties of the generalized band matrices. The theoretical results are enlightened by a large number of figures illustrating numerical examples.
Url:
DOI: 10.1007/BF02575869
Affiliations:
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R Zsa</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:885B24257E2A294B1FF970140A5C489F9B642190</idno><date when="1991" year="1991">1991</date><idno type="doi">10.1007/BF02575869</idno><idno type="url">https://api.istex.fr/document/885B24257E2A294B1FF970140A5C489F9B642190/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001C64</idno><idno type="wicri:Area/Istex/Curation">001C64</idno><idno type="wicri:Area/Istex/Checkpoint">001192</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001192</idno><idno type="wicri:doubleKey">0008-0624:1991:Favati P:generalized:band:matrices</idno><idno type="wicri:Area/Main/Merge">001770</idno><idno type="wicri:Area/Main/Curation">001673</idno><idno type="wicri:Area/Main/Exploration">001673</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Generalized band matrices and their inverses</title><author><name sortKey="Favati, P" sort="Favati, P" uniqKey="Favati P" first="P." last="Favati">P. Favati</name><affiliation wicri:level="3"><country xml:lang="fr">Italie</country><wicri:regionArea>IEI-CNR, Via S. Maria 46, 56100, Pisa</wicri:regionArea><placeName><settlement type="city">Pise</settlement><region nuts="2">Toscane</region></placeName></affiliation></author><author><name sortKey="Lotti, G" sort="Lotti, G" uniqKey="Lotti G" first="G." last="Lotti">G. Lotti</name><affiliation wicri:level="1"><country xml:lang="fr">Italie</country><wicri:regionArea>Dipartimento di Matematica, University of Trento, 38050, Povo (TN)</wicri:regionArea><wicri:noRegion>Povo (TN)</wicri:noRegion></affiliation></author><author><name sortKey="Romani, F" sort="Romani, F" uniqKey="Romani F" first="F." last="Romani">F. 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R Zsa</name><affiliation wicri:level="3"><country xml:lang="fr">Hongrie</country><wicri:regionArea>Department of Mathematics, Technical University of Budapest, Stoczek-u. 2-4, 1111, Budapest</wicri:regionArea><placeName><settlement type="city">Budapest</settlement><region nuts="2">Hongrie centrale</region></placeName></affiliation></author></analytic><monogr></monogr><series><title level="j">CALCOLO</title><title level="j" type="abbrev">Calcolo</title><idno type="ISSN">0008-0624</idno><idno type="eISSN">1126-5434</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Milan</pubPlace><date type="published" when="1991-03-01">1991-03-01</date><biblScope unit="volume">28</biblScope><biblScope unit="issue">1-2</biblScope><biblScope unit="page" from="45">45</biblScope><biblScope unit="page" to="92">92</biblScope></imprint><idno type="ISSN">0008-0624</idno></series><idno type="istex">885B24257E2A294B1FF970140A5C489F9B642190</idno><idno type="DOI">10.1007/BF02575869</idno><idno type="ArticleID">Art4</idno><idno type="ArticleID">BF02575869</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0008-0624</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The idea of defining the generalized band matrices is based on the recognition that several pattern matrices and their inverses have low rank submatrices in certain domains. Theoretical considerations concerning the generalized band matrices enable us to give uniform treatment for several well known classes of matrices like band matrices, block band matrices, band matrices with low rank corrections, sparse matrices and their inverses. Making use of the new notions of information content and of compact representation of matrices, the concept of proper matrices is extended for generalized band matrices. Some reduction algorithms are presented which help to discover certain hidden structural properties of the generalized band matrices. The theoretical results are enlightened by a large number of figures illustrating numerical examples.</div></front></TEI><affiliations><list><country><li>Hongrie</li><li>Italie</li></country><region><li>Hongrie centrale</li><li>Toscane</li></region><settlement><li>Budapest</li><li>Pise</li></settlement><orgName><li>Université de Pise</li></orgName></list><tree><country name="Italie"><region name="Toscane"><name sortKey="Favati, P" sort="Favati, P" uniqKey="Favati P" first="P." last="Favati">P. Favati</name></region><name sortKey="Lotti, G" sort="Lotti, G" uniqKey="Lotti G" first="G." last="Lotti">G. Lotti</name><name sortKey="Romani, F" sort="Romani, F" uniqKey="Romani F" first="F." last="Romani">F. Romani</name></country><country name="Hongrie"><region name="Hongrie centrale"><name sortKey="R Zsa, P" sort="R Zsa, P" uniqKey="R Zsa P" first="P." last="R Zsa">P. R Zsa</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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